Question

# In given figure diagonal AC of a quadrilateral, ABCD bisects the angles $$\angle A$$ and $$\angle C$$. Prove that AB = AD and CB = CD.

Solution

## Since diagonal AC bisects the angles $$\angle A$$ and $$\angle C$$,we have $$\angle BAC = \angle DAC$$ and $$\angle BCA = \angle DCA$$.In triangles ABC and ADC, we have$$\angle BAC = \angle DAC$$   (given);$$\angle BCA = \angle DCA$$    (given);AC = AC     (common side).So, by ASA postulate, we have$$\triangle BAC \cong \triangle DAC$$$$\Rightarrow$$ BA = AD and CB = CD    (Corresponding parts of congruent triangle).Mathematics

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